\subsection[Maximum Sustainable Benefits to Avoid Operating Losses]{Maximum Sustainable Benefits to Avoid Operating Losses}
\label{sec:MaximumSustainableBenefitstoAvoidOperatingLosses}

Insurers' Maximum Sustainable Benefit For Avoiding Losses\index{Maximum Sustainable Benefit For Avoiding Losses}, \textbf{$MSBAL_N$}\index{$MSBAL_N$}, are the highest portions of premium dollars they can provide, as benefits, throughout the year, while matching $PI$'s probability (0.9772) of avoiding operating losses. To adjust for their differences in PLRE variability, $MSBAL_{NHI}$ = 0.8500 - 2 * $\sigma_{e_{N}}$ because PLREs above 0.8500 produce operating losses. Table~\ref{tab:InsurerOperatingResultsByPortfolioSize} Row 13, shows that $MSBAL_{NHI}$ = 0.8443; $MSBAL_{B}$ = 0.8184; and $MSBAL_{PI}$ = 0.7500. $MSBAL_{D}$ = 0.5338 and because $\sigma_{e_{E}}$ is ten times larger than $\sigma_{e_{PI}}$, $MSBAL_{E}$ is less than 0.0000 (0.8500 - 2 * 0.5000), because $E$'s probability of losses (0.4207) is much higher than PI's (0.0228). 

Insurers' Maximum Average Benefits Per Policyholder To Avoid Operating Losses\index{Maximum Average Benefits Per Policyholder To Avoid Operating Losses} \textbf{$MABPPL_N$}\index{$MABPPL_N$} are the highest benefits, in dollars, ($MABPPL_{N}$ = $MSBAL_{N}$ * \$4,000) insurers can pay, while matching $PI$'s probability (0.9772) of avoiding operating losses. Table \ref{tab:InsurerOperatingResultsByPortfolioSize} Row 14, lists these benefits. $MABPPL_{NHI}$ = \$3,377, $MABPPL_{B}$ = \$3,274 and $MABPPL_{PI}$ = \$3,000. $MABPPL_{D}$ = \$2,135 and $MABPPL_{E}$ $<$ \$0.00.

Matching $PI$'s ability to earn profits is easier than matching $PI$'s ability to avoid losses, because the more loss smaller insurers are, the more they need to cut benefits, to match $PI$'s probability of avoiding losses. $PI$', $D$'s and $E$'s probabilities of earning profits, or incurring losses, are similar near the PLR, but rapidly diverge above the PLR, making it increasingly more difficult to match $PI$'s performance. %causing the(1.0000 - $\Phi_{C}(0.8000)$) = 0.1587) is modestly higher than 0.6241 ((1.0000 - $\Phi_{D}(0.8000)$)) and 0.5398 (1.0000 - $\Phi_{E}(0.8000)$), while 0.0228 ($1.0000 - \Phi_N(0.9000)$), is much lower than 0.1714 (1.0000 - $\Phi_{E}(0.8000)$) and 0.3821 (1.0000 - $\Phi_{E}(0.8000)$). It is much harder for D and E to meet the constraint than for PI or larger insurers. T  